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If you are in the process of cooking st home and no cream is at hand, you can use milk and a flour roux to thicken. SeaJambon is right...you need the fat in the cream for a thick, lucious sauce. BUT, if you are looking for a fix, use 2TBSP of butter and 2-3 TBSP of flour, make a bit if a roux, add milk. You need to cook the flour for a few minutes before adding your cheese...not as good, but "good enough" if in a pinch

A note about Alfredo. Yes, it does require cream in the modern version. But although fettucine alfredo originated in Rome, the Romans have all but disowned it. There are places which will sell the dish to tourists who have fond memories of Olive Garden but hardly a single contemporary Roman cookbook bothers to mention it. It's origin is fettucine with "triple butter" which really is authentically Roman. A lot of butter and a lot of cheese and Romans do love fettucine.

You don't need the cream. As Pierino noted, the original sticks with butter, pasta water, and cheese.

You can make any sauce containing cheese thick and creamy. Think about what. What's in cheese? The same thing found in cream.....

Melt your butter, stir in some reserved pasta water (after cooking your pasta in it), once emulsified, stir in your grated Parmigiano-Reggiano. Let it cook as you whisk, add a touch of salt and fresh cracked pepper. I promise your Alfredo sauce will be perfectly thick, rich, and creamy.